The present invention relates to an image reconstructing method for X-ray CT (Computed Tomography) apparatuses, for instance, and an X-ray CT apparatus.
When image reconstruction of projection data obtained by such as helical scanning, conventional scanning (axial scanning) and cine scanning (scanning of the same position in three directions a plurality of times to obtain tomograms at different points of time) based on a three-dimensional back projection method is to be accomplished, an X-ray CT apparatus is known which performs image reconstruction on the basis of intact projected data on each row of a multi-row detector (see JP-A No. 2001-for instance).
The apparatus of the above-described configuration was unable to perform control of slice thicknesses as consecutive values in the Z-direction, noise control or artifact control.
Regarding the slice thickness, it differs between the central part and the peripheral parts of image reconstruction, and it is impossible to control slice thicknesses in positions within the tomogram plane.
In three-dimensional image reconstruction by the X-ray CT apparatus, to calculate pixel data of the pixels of an image by using X-ray detector data corresponding to not only the X-direction but also the Z-direction, its hardware adaptation is considered, in order to be compatible with various applications which require specific pixels to have a plurality of rows of information, it is necessary to carry three-dimensional back-projection processing a plurality of times according to the quantity of that information. However, this is a redundant calculation.
Thus, image reconstruction hardware having no flexibility cannot freely back-project projection data of each row onto a given pixel.
For this reason, when a plurality of rows of projection data of different from that pixel are to be subjected to back projection processing, the back projection processing should be performed a plurality of times according to the geometrical condition of data collection for that plurality of rows of projection data (the positional relationship among the X-ray generation source, the X-ray detector and the subject).
In order to solve the problem noted above, what was considered necessary a three-dimensional image reconstruction algorithm which would permit back projection processing in one round by adding projection data of rows of different data collection geometries in a projection data space.
More specifically, as shown in FIG. 16 for instance, the spherical focus of an X-ray tube 21, an X-ray detector 24 and the X, Y and Z axes are defined. The X-ray tube 21 and the detector 24 shown in FIG. 16 rotate around the Z-axis.
FIG. 17 is a view of the configuration shown in FIG. 16 as seen in the direction of the X-axis. In other words, it is a YZ plane.
It has to be noted that this FIG. 17 shows one example of specific view time when an image is to be produced in a position away by ofz (off-center in z direction; also referred to as dz) from the center of the detector in the Z-direction at the time of conventional (axial) reconstruction or helical reconstruction.
The image position in which reconstruction is to be done in the direction of the Z-axis then as shown in FIG. 17 is represented by a reconstruction plane p. In FIG. 17, out of the straight lines L linking the X-ray focus of the X-ray tube 21 and the X-ray detector 24, only what passes the reconstruction plane p is shown.
Only the pixels on the reconstruction plane p which this straight line L passes are directly relevant to data detected by the detector 12, and data on all other pixels are created by weighted addition of detector data between which each such pixel is positioned.
FIG. 18 is a view of the reconstructed plane shown in FIG. 17 from the xy plane.
In more detail, pixels in the parts corresponding to equal distances from the X-ray tube 21 are directly relevant to X-ray detector data, and data on all other pixels are created by weighted addition of detector data between which each such pixel is positioned. One row of projection line of a multi-row X-ray detector having a curve such as what is shown in FIG. 18 will be referred to as real arciform projection data rd.
FIG. 19 is a diagram showing the geometrical relationship among virtual detector data vd, the X-ray focus, the detector and the reconstruction plane.
In the three-dimensional image reconstruction, the virtual detector data vd indicated by dotted lines as shown in FIG. 19 for instance are created from the real detector data rd indicated by solid lines as shown in FIG. 18 for instance. Thus, the virtual arciform projection data vd are created from the real arciform projection data rd.
These virtual projection data vd indicated by dotted lines can make it look as if data were collected in such a configuration.
Such virtual projection data vd indicated by dotted lines can be created from the real X-ray detector data rd indicated by solid lines by weighted addition processing or otherwise.
Viewed from the YZ plane, the virtual detector data vd indicated by dotted lines have a configuration such as shown in FIG. 20 for instance. Of viewed from the xy plane, they have a configuration such as shown in FIG. 21 for instance.
By creating the above-described virtual data vd from the real X-ray detector data rd by weighted addition processing or otherwise, inputting them as input data to three-dimensional image reconstruction hardware, and providing the three-dimensional image reconstruction hardware with information of such a virtualized detector configuration, data of the X-ray detector configuration as shown in FIG. 17 for instance, an image can be reconstructed in the X-ray detector configuration as shown in FIG. 20.
Further, where two reconstruction planes p1 and p2 are defined and added to each other as shown in FIG. 22 for instance, in three-dimensional image reconstruction three-dimensional image reconstruction is processed two times to reconstruct two images and those images are added.
However, it is redundant to perform three-dimensional image reconstruction two times. Since the addition can be accomplished in the projection data space, it is possible to reduce the processing quantity of three-dimensional image reconstruction.
In actual operation, regarding the reconstruction plane p1, the real arciform projection data rd are obtained as shown in FIGS. 23(a) and (b) for instance.
Regarding the reconstruction plane p2, the virtual arciform projection data vd are created as shown in FIGS. 24(a) and (c) for instance.
For instance, since the virtual arciform projection data vd shown in FIGS. 24(a) and (c) are so subjected to weighted addition as to be identical with the real arciform projection data rd shown in FIG. 23(b) and FIG. 24(b), it is possible to add the projections of the reconstruction planes p1 and p2 before the three-dimensional image reconstruction, and therefore the processing of three-dimensional image reconstruction to add the two reconstruction planes can be accomplished in one round.
Furthermore, as many planes of projection data can be added as desired, and it is also possible to use weighting to add them in any desired balance and thereby accomplish weighted addition. Similar effects can be obtained with parallel projection data as well.
Two problems will be discussed below.
[Problem iith Image Reconstruction Hardware without Flexibility]
As described above, in the hardware adaptation of three-dimensional image reconstruction, it is not possible to process three-dimensional back-projection by freely creating virtual arciform projection data from projection data of different rows in various patterns for each view.
In other words, what are compatible with a hardware adaptation of three-dimensional image reconstruction are general helical projection data or conventional (axial) projection data in which virtual arciform projection data are absent.
For such helical projection data, the moving speed of the table is figured out from the helical pitch information, the width of each X-ray detector in the Z-direction and the number of detector rows.
However, such items of information are fixed until the photographic conditions are once determined for a sequence of data, and the geometric system of three-dimensional image reconstruction is determined by the distance dz from the center of the detector row to the Z-position of the image to calculate and determine the parameters of three-dimensional image reconstruction.
The expression of that geometric system on the xy plane would be as shows in FIGS. 25(a) through (f) for instance. In FIGS. 25(a) through (f), for the sake of brevity of description, the rotating direction is expressed in a fixed angle, but in reality its right form is a state of having rotated by an equivalent of the angle in the rotational direction on the xy plane.
In the above-described case, dz in the Z-direction varies according to the view, and the position of one-row equivalent of arciform projection data matching the reconstruction plane on the xy plane varies according to that dz.
In other words, the greater the absolute value of dz, the denser the one-row equivalent of arciform projection data on the reconstruction plane p, and the smaller the value of dz, the sparser the data.
Thus in the three-dimensional image reconstruction hardware having no flexibility, the X-ray geometric system in each view is fixed by the given helical pitch, the thickness of the detector cells in the Z-direction and the number of slices.
Similarly in conventional (axial) scanning as well, its X-ray geometric system, namely the relative density of the arciform projection data on the reconstruction plane is fixed by dz.
Thus, arciform projection data cannot be effectively utilized in three-dimensional image reconstruction hardware (or software) with no flexibility of creating virtual arciform projection data as desired. As a result, no tomogram of adequate picture quality can be subjected to image reconstruction.
For this reason, there is a call for an apparatus which can reconstruction images of high accuracy by using arciform projection data on image reconstruction hardware (or software).
[Inconsistency in Weighting of Back Projection Processing by Feldkamp Reconstruction Method]
Incidentally, in a common three-dimensional image reconstruction algorithm or a common Feldkamp image reconstruction algorithm, there is a problem of inconsistency in the weighting of the cone beam reconstruction weighting coefficient. This is due to the relative density of arciform projection data dependent on the value of dz as stated above.
In more detail, in an image reconstruction algorithm which uses opposed data by subjecting weighted addition to the opposed data, it does so by subjecting to weighted addition data to be projection on pixels on the reconstruction plane by using data differing in phase by 180 degrees. There will arise an inconsistency unless the sum of different weighting functions at the time of creation by weighted addition is 1.0, resulting in an inconsistency in the uniformity of artifacts and CT values on the tomogram.
For instance, pixels which have no direct match in the arciform projection data rd on the reconstruction plane p shown in FIG. 25 and are positioned between the arciform projection data rd are created by weighted addition from the arciform projection data rd between which the pixels are positioned.
When the weighting function of the cone beam reconstruction weighting coefficient at the time varies steeply, if there is a different in relative density from the opposed data, the sum of weighting functions of pixels will differ from 1.0. This results in an inconsistency in weighting.
Description will be made with reference to FIG. 26. As shown therein, pixels positioned between arciform projection data with weighted addition are subjected to image reconstruction after creation by weighted addition with the arciform projection data between which the pixels are positioned. Therefore, if the weighting function of the cone beam reconstruction weighting coefficient is already applied to the arciform projection data, the weighting coefficient of the cone beam reconstruction weighting coefficient is also figured out by weighted addition at the same time.
If this weighted addition is linear weighted addition and the weighting function of the original cone beam reconstruction weighting coefficient is nonlinear, there will arise a difference from the linear weighted addition, resulting in an inconsistency.
Where, for instance, weighting with the cone beam reconstruction weighting coefficient is calculated for each pixel at the time of three-dimensional image reconstruction or weighted addition similar in shape to the weighting function is done, there will arise no inconsistency, but such processing would require complex three-dimensional image reconstruction processing. Thus, the load of calculation would become too great to be realistic.
For this reason, a common Feldkamp image reconstruction algorithm involves the problem of inconsistency with respect to weighting.
An object of the present invention is to improve the problems noted above and provide an image reconstructing method and an X-ray CT apparatus for the processing of three-dimensional image reconstruction capable of achieving image reconstruction of tomograms of high picture quality or image reconstruction of tomograms of desired picture quality.